replace Hitachi hard-drive

What 1TB or bigger hard drive can I use to replace the Hitachi HDS721010KLA330 1TB hard drive P/N 0A37893 in my 24" iMac? Do I need to shop by P/N, or is the model number sufficient?

Model number is sufficient.
You just need the HD size and Sata version actually, well usually.
2.5" is usually for Laptops and 3.5" are for desktops.
By the way you can still get the same Hitachi HD if you go to Amazon or NewEgg for example. Your drive is a Sata ll, runs at 3Gb/ps, is a 3.5 inch HD and runs at 7200 rpms. Sata is backward compatible so if you get a 6gb/ps one (Sata lll) it will just run at the lower 3gb/ps speed.
Western Digital (WD), Seagate, Samsung, and Toshiba are just some of the name brands you can also buy.

I can highly recommend the WD Black 3.5" 7200 HDDs.

Sometimes just a few dollars more than ordinary HDDs but they run cool and fast and come with a five year warranty. They are basically Enterprise quality HDDs.